Scilab Function
Last update : Dec 1997

cdfnor - cumulative distribution function normal distribution

### Calling Sequence

  `[P,Q]=cdfnor("PQ",X,Mean,Std)`
  `[X]=cdfnor("X",Mean,Std,P,Q)`
  `[Mean]=cdfnor("Mean",Std,P,Q,X)`
  `[Std]=cdfnor("Std",P,Q,X,Mean)`

### Parameters

- `P,Q,X,Mean,Std`: six real vectors of the same size.
- `P,Q (Q=1-P)` : The integral from -infinity to X of the normal density. Input range: (0,1].
- `X`:Upper limit of integration of the normal-density. Input range: ( -infinity, +infinity)
- `Mean`: The mean of the normal density. Input range: (-infinity, +infinity)
- `Sd`: Standard Deviation of the normal density. Input range: (0, +infinity).

### Description

Calculates any one parameter of the normal distribution given values for the others.

A slightly modified version of ANORM from Cody, W.D. (1993). "ALGORITHM 715: SPECFUN - A Portabel FORTRAN Package of Special Function Routines and Test Drivers" acm Transactions on Mathematical Software. 19, 22-32. is used to calulate the cumulative standard normal distribution.

The rational functions from pages 90-95 of Kennedy and Gentle, Statistical Computing, Marcel Dekker, NY, 1980 are used as starting values to Newton's Iterations which compute the inverse standard normal. Therefore no searches are necessary for any parameter.

For X < -15, the asymptotic expansion for the normal is used as the starting value in finding the inverse standard normal. This is formula 26.2.12 of Abramowitz and Stegun.

The normal density is proportional to exp( - 0.5 * (( X - MEAN)/SD)**2)

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.